Parametrization of local CR automorphisms by finite jets and applications Academic Article uri icon

abstract

  • For any real-analytic hypersurface M C N Msubset mathbb {C}^N , which does not contain any complex-analytic subvariety of positive dimension, we show that for every point p M pin M the local real-analytic CR automorphisms of M M fixing p p can be parametrized real-analytically by their p ell _p jets at p p . As a direct application, we derive a Lie group structure for the topological group Aut ( M , p ) operatorname {Aut}(M,p) . Furthermore, we also show that the order p ell _p of the jet space in which the group Aut ( M , p ) operatorname {Aut}(M,p) embeds can be chosen to depend upper-semicontinuously on p p . As a first consequence, it follows that given any compact real-analytic hypersurface M M in C N mathbb {C}^N , there exists an integer k k depending only on M M such that for every point

published proceedings

  • Journal of the American Mathematical Society

author list (cited authors)

  • Lamel, B., & Mir, N.

citation count

  • 16

complete list of authors

  • Lamel, Bernhard||Mir, Nordine

publication date

  • April 2006